Problem: Simplify the following expression: $y = \dfrac{z^2 - 5z + 4}{z - 4} $
Answer: First factor the polynomial in the numerator. $ z^2 - 5z + 4 = (z - 4)(z - 1) $ So we can rewrite the expression as: $y = \dfrac{(z - 4)(z - 1)}{z - 4} $ We can divide the numerator and denominator by $(z - 4)$ on condition that $z \neq 4$ Therefore $y = z - 1; z \neq 4$